I have a very old, 1950's, tea cup and saucer from Disneyland. A Miokey & Minnie Mouse salt & pepper shaker set from Disneyland. And an original Big Al Plush that was sold at Disneyland the year the County Bear Jamboree opened. All plush, no plastic face and he is cool.
I have a 1979 Disney, Blue with Gold trim, Trucker hat that has my name embroidered in it. Even today, since trucker hats have come back in, I break it out and wear it. I also have a Disney Park map, and Ride tickets from that trip. I was six years old at the time!
I have several things from the 70's
A big Al beer stein, some old coupon books, (no e-tickets of course).
and some more stuff like that. But my prize posession is a 1957 Fantasyland pennant. It is framed in glass, and it is in nearly perfect condition. It has the dumbo ride printed on it.
I have a guide book from 1961 (purchased on eBay) in like new condition. The oldest from my personal collection would be two items; a porcelain Castle bank from my first trip to DL back in 1967 and a porcelain "Happy" Dwarf barrel shaped pencil sharpener (from the same trip). Both in as-new condition.
I have a 1982 Mickey Mouse doll dressed up as Santa. My parents bought it the year I was born. Aside from missing one eyebrow, he is in very good shape (much like the OP tigger). I also had maps from every year that I went, but those are misplaced